We prove that the Hopf vector field is unique among geodesic unit vector fields on spheres such that the submanifold generated
by the field is totally geodesic in the unit tangent bundle with Sasaki metric. As an application, we give a new proof of
stability (instability) of the Hopf vector field with respect to volume variation using standard approach from the theory
of submanifolds and find exact boundaries for the sectional curvature of the Hopf vector field.